Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19621 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#19634 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C23×C11 | #127 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,23)(16,18)(17,22)(19,24)(21,26)(25,27)(28,29,32,35)(30,36,39,43)(31,40,37,34)(33,41,42,38);(12,14,15,22,16,21,24,27)(13,17,19,20,18,25,23,26);(13,18)(17,25)(19,23)(20,26)(28,30,37,41,32,39,31,38)(29,33,40,43,35,42,34,36);(14,21)(17,25)(20,26)(22,27)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12622);